Unconventional Universal Computation in Babbage's Analytical Engine

TL;DR

This paper demonstrates that Babbage's Analytical Engine, despite its unconventional design, can theoretically perform universal computation by implementing indirect addressing, enabling simulation of a Turing machine with a fixed memory size.

Contribution

It introduces a method to implement indirect addressing in the Analytical Engine, showing its theoretical universality beyond original design limitations.

Findings

Analytical Engine can simulate a Turing machine with fixed memory.

Indirect addressing can be implemented in the Analytical Engine.

The work is of theoretical and historical interest, not practical use.

Abstract

This paper shows that the programming model of Babbage's Analytical Engine, although unconventional, can be harnessed in order to simulate indirect addressing, a capability that was not included in the original instruction set. That is, in a theoretical sense, the Analytical Engine was as universal as computers we have today. We show how to implement indirect addressing for a working memory of fixed size; this makes it possible to simulate a Turing machine with a finite tape. The result is, of course, only of theoretical and historical interest, without any practical implications.